We provide exact analytical solutions for the magnetic field produced by prescribed current distributions located inside a toroidal filament of finite thickness. The solutions are expressed in terms of toroidal functions, which are modifications of the Legendre functions. In application to the MHD equilibrium of a twisted toroidal current loop in the solar corona, the Grad–Shafranov equation is decomposed into an analytic solution describing an equilibrium configuration against the pinch-effect from its own current and an approximate solution for an external strapping field to balance the hoop force. Our solutions can be employed in numerical simulations of coronal mass ejections (CMEs). When superimposed on the background solar coronal magnetic field, the excess magnetic energy of the twisted current loop configuration can be made unstable by applying flux cancellation to reduce the strapping field. Such loss of stability accompanied by the formation of an expanding flux rope is typical for the Titov & Démoulin eruptive event generator. The main new features of the proposed model are as follows: the filament is filled with finite
The magnetic fields of interplanetary coronal mass ejections (ICMEs), which originate close to the Sun in the form of a flux rope, determine their geoeffectiveness. Therefore, robust flux rope‐based models of CMEs are required to perform magnetohydrodynamic (MHD) simulations aimed at space weather predictions. We propose a modified spheromak model and demonstrate its applicability to CME simulations. In this model, such properties of a simulated CME as the poloidal and toroidal magnetic fluxes, and the helicity sign can be controlled with a set of input parameters. We propose a robust technique for introducing CMEs with an appropriate speed into a background, MHD solution describing the solar wind in the inner heliosphere. Through a parametric study, we find that the speed of a CME is much more dependent on its poloidal flux than on the toroidal flux. We also show that the CME speed increases with its total energy, giving us control over its initial speed. We further demonstrate the applicability of this model to simulations of CME‐CME collisions. Finally, we use this model to simulate the 12 July 2012 CME and compare the plasma properties at 1 AU with observations. The predicted CME properties agree reasonably with observational data.
more » « less- NSF-PAR ID:
- 10375434
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Space Weather
- Volume:
- 18
- Issue:
- 5
- ISSN:
- 1542-7390
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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